The "Av-Matoran get inexplicable psychic powers" explanation makes sense, though it certainly makes BIONICLE's power system feel a bit arbitrary.
The strictly correct answer to the original question is that Templar Studios probably came up with it as a way to explain the climactic cutscenes.
As BIONICLE lost its initial grounding in mystical elements, I feel like it shifted into science fiction territory a little bit. BIONICLE has always had something of a hard magic system for the Toa, but at first it was far vaguer for everything else. Makuta, the Great Spirit, the prophesies... all of these things existed and had effects on the plot, but no one knew how they worked. Then as BIONICLE entered into the "grittier" phase in the Mask of Life arc, answering a number of those questions contributed to a de-mystification of the previously fantastical world.

There is an interesting "what if" for alternate universe characters here. What if there was an AU in which Tahu was a Toa of Air? Or water? I don't remember whethe BIONICLE has infinite alternate universes, but I get the sense that there are enough that this kind of thing could happen.
Sounds like the premise to a really good or really bad fanfic.

I'll have to take a look at that. For right now, all of the rules docs are pinned in the general text channel of the discord.
The game was initially designed as a sort of high-commitment board game, where once players learned the rules it's easy to play pickup games. I do have plans in the works for a traditional RPG using this system--including noncombat skills, level progression, etc.--but that's relatively unrefined at the moment. My dream is to eventually stream a BIONICLE rpg on twitch or post videos of sessions on YouTube, similarly to D&D.

Have you ever wanted to lead the bohrok swarms against the vahki hordes? Perhaps you would like to see Garan and Tanma recruited into the Chronicler's Company? Perhaps you'd like to lead a coalition of Toa, or Turaga, or Piraka, or a smattering of everything? Well I have the game for you!
Conflux is a dice-based combat system that uses a grid to track character location and movement. In a lot of ways it feels like D&D, albeit with different mechanics. Characters usually attack and defend using some number of dice and take damage equal to the difference if the attacker rolls higher. There is, of course, a fair amount to the game beyond that, which is covered in the attached rules docs.
The game was originally designed as a face-to-face strategy game, but with recent events, I have decided to make the jump to playing online over discord. Consider this a recruitment pitch! If you would like to join me sometime, here's the discord link:
https://discord.gg/vJcs3DB
If anyone uses the system on their own, please let me know how it goes! My collection is by no means comprehensive, so not everything in the game is well-tested. For similar reasons, not everything in the BIONICLE canon has been statted out. If you have any ideas to contribute for that, then feel free to post them here!
Here's the current rules draft:
https://www.dropbox.com/s/iiloxlnbgvcsv3l/How to Play.docx?dl=0
https://www.dropbox.com/s/no3qwj72ye48mjm/2001-2003 5.3.docx?dl=0
https://www.dropbox.com/s/8dh00nbs28tfo6j/2004-2005 5.3.docx?dl=0
https://www.dropbox.com/s/z4aifnfgxo98od8/2006-2008 5.3.docx?dl=0
https://www.dropbox.com/s/bg36d867o77t5bb/2009-2010 5.3.docx?dl=0
2009-2010 5.3.docx
How to Play.docx 2006-2008 5.3.docx 2004-2005 5.3.docx 2001-2003 5.3.docx

This is a remarkable retelling of the BIONICLE story. It reminds me of SAO Abridged, in which the original is so thoroughly deconstructed that the result is a deeper and more coherent narrative. I especially like Takua's character. The MNOG is by far the best part of BIONICLE and even without the mind-wipe, your presentation of Takua is more faithful to his characterization in the game than any other part of the BIONICLE canon.
The art style is also brilliant. Scaling back on detail overall makes the more intricate parts--like Tahu's chest--stand out more.
Great work, and I look forward to seeing more.

Vakama stiffened. That heat signature was almost certainly Nidhiki. His eyes cut back and forth through the sculpture fields. The Hunters may be deadly, but Nidhiki wasn’t likely to attack in the open.
“What is it, Toa?”
“Nothing, Ahkmou.”
He looked entirely unconvinced. Go figure.
“Vakama! I’ve found the disk, but it’s wedged pretty tight. I’m going to have to pull it out with both hands.”
“Use your stone powers!”
“How?”
“Forget it, just pull it out.”
The raw physical strength of a Toa of Stone was enough to shake the pyramid to its foundations… which was unfortunate for Onewa. As Onewa gave a grunt of satisfaction, the structure began to keel over.
“Change of plans. Nuhrii, watch Ahkmou!”
ChhhhhhhhhWHOOOOM!!!
Vakama ignited his disk launcher’s jet packs and surged into the air. He caught Onewa as he began to fall and angled out of the path of the falling sculpture. The two Matoran were running to avoid the cloud of dust and debris. Onewa was saying something, but Vakama couldn’t make it out over the rush of wind. They landed in front of the two startled Matoran. Vakama closed his eyes and focused. No trace of Nidhiki. Unfortunate. Had he tipped his hand too early? Hopefully not. All that Nidhiki saw was an unusually well-adjusted new Toa. He would have to be more careful.
“Hey! I’m talking to you!”
“Oh, sorry Onewa.”
“Sorry doesn’t cut it. How did you just fly? Isn’t that a Toa of Air thing? What’s the deal?”
Careful. He needed these Toa if he was going to take on a Makuta. Accursed heat resistance...
“It’s a trick Toa Lhikan told me about.” That’s a lie that Onewa couldn’t check right now. It’d have to do. “He said that a highly focused stream of fire could give the necessary propulsion for flight.”
“Hmm…” Onewa gave him a dubious sideways glance. “Everyone’s seen Lhikan flying, but there was never any trail of fire or anything.”
“I guess he’s just much better at it.”
“But that still doesn’t explain how easily you’ve mastered your powers. I can’t figure out how to use any of my powers.”
“Ah. Well I don’t know why it’s so much easier for me, but I can give you some pointers if you’d like.”
Nidhiki watched the four figures exiting the Sculpture fields. That fire Toa was something else… but he’d drop his guard eventually. Green Toa always do, even the hotshots. And then he would strike. Nidhiki’s mandibles made his smile grotesque. The hunt was on.